### Abstract

In this paper, we introduce a new detector referred to as Geometric mean detector (GEMD) which is based on the ratio of the largest eigenvalue to the Geometric mean of the eigenvalues for collaborative spectrum sensing. The decision threshold has been derived by employing Gaussian approximation approach. In this approach, the two random variables, i.e. the largest eigenvalue and the Geometric mean of the eigenvalues are considered as independent Gaussian random variables such that their cumulative distribution functions (CDFs) are approximated by a univariate Gaussian distribution function for any number of cooperating secondary users and received samples. The approximation approach is based on the calculation of exact analytical moments of the largest eigenvalue and the Geometric mean of the eigenvalues of the received covariance matrix. The decision threshold has been calculated by exploiting the CDF of the ratio of two Gaussian distributed random variables. In this context, we exchange the analytical moments of the two random variables with the moments of the Gaussian distribution function. The performance of the detector is compared with the performance of the energy detector and eigenvalue ratio detector. Analytical and simulation results show that our newly proposed detector yields considerable performance advantage in realistic spectrum sensing scenarios. Moreover, our results based on proposed approximation approach are in perfect agreement with the empirical results.

Original language | English |
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Title of host publication | IEEE GLOBECOM Workshops (GC Wkshps), 2011 |

Place of Publication | Houston, TX, USA |

Publisher | IEEE |

Pages | 913-917 |

Edition | 2011 |

ISBN (Electronic) | 978-1-4673-0040-7, 978-1-4673-0038-4 |

ISBN (Print) | 978-1-4673-0039-1 |

DOIs | |

Publication status | Published - 2011 |

Externally published | Yes |

### Publication series

Name | IEEE GLOBECOM Workshops (GC Wkshps) |
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Publisher | IEEE |

ISSN (Print) | 2166-0077 |

### Keywords

- Spectrum sensing
- Geometric mean detector (GEMD)
- moments of largest eigenvalue
- moments of Geometric mean of eigenvalues
- Gaussian approximation approach

## Cite this

Shakir, M. Z., Rao, A., & Alouini, M-S. (2011). Collaborative spectrum sensing based on the ratio between largest eigenvalue and Geometric mean of eigenvalues. In

*IEEE GLOBECOM Workshops (GC Wkshps), 2011*(2011 ed., pp. 913-917). (IEEE GLOBECOM Workshops (GC Wkshps)). IEEE. https://doi.org/10.1109/GLOCOMW.2011.6162590